1. ES 128 Computational Solid and Structural Mechanics

2. ES128 - Computational Solid & Structural Mechanics
Introduction to Finite Elements
Focus on computer analysis using the commercial code ABAQUS
Tuesday-Thursday: 1 pm pm + computer lab
Cruft 309

3. Introducing ourself Instructor: Katia Bertoldi
Office: Pierce 311
Office hours: Thursday 3 pm - 4 pm
TF: Johannes (Bas) Overvelde
Office: Pierce 404
Office hours: Wednesday 5 pm - 6 pm

4. Introducing yourself

5. Introduction What do l learn in ES128? Why is ES128 important for me?
How is ES128 organized?

6. What do I learn in ES128?
Prerequisite: ES120 and ES123 You will learn computational techniques for the simulation of a large variety of engineered systems. The application to real engineering applications are stressed throughout. Introduction to finite element methods for analysis of steady-state and transient problems in solid, structural, fluid mechanics, and heat transfer. We will model problems involving fluids and solids and learn how to interpret the numerical results.

7. What do I learn in ES128?
Focus on computer analysis using the finite-element method. In computer implementation, you will develop simple finite-element analyses using Matlab and the general-purpose program ABAQUS. You will do a project addressing a significant problem arising in engineering, biomechanics or earth science

8. Why is ES128 important?
Many engineering problems can be described in terms of partial differential equations
The finite element method is a numerical approach to solve approximately these partial differential equations
FEM is used by million of scientist worldwide.

9. Why is ES128 important?
In engineering practice, analysis is largely performed with the use of finite element computer programs (such as ABAQUS, NASTRAN, ANSYS, ADINA, SIMULIA, COMSOL etc…)
These analysis programs are interfaced with computer-aided design ( CAD) programs Catia,g ) p g , SolidWorks, Pro/Engineer, NX, etc.

10. Why is ES128 important?
Computations are everywhere in engineering problems.
Many problems are resolved with the aid of computers and dedicated programs today. It is important to be able to implement numerical algorithms

11. How is ES128 organized? Spring 2010: Tue – Thu –1:00 pm - 2:30 pm
Lab session: weekly – to be organized
Office hours: Katia Thu 3 pm -4 pm
Bas Wednesday 5 pm– 6 pm
Textbook: A First Course in Finite Elements
Jacob Fish, Ted Belytschko

12. Lab session
When?
How?

13. How is ES128 organized? The grade comes from four components
Each component contributes ¼ to the course grade.
Homework (25%)
One assignment week (assigned and due on Thursday). Combination of problem sets and computer exercises
Project (25%)
2 Midterms (25% each)

14. ES 128 Project
You will work in a group of 2-3 students on a project that
addresses a phenomenon or engineering design issue, and
involves serious use of FEM.
(Step 1) Each student presents a project proposal (Feb 20 in class)
5 minute presentation. On 2 slides you should explain
What is the project? What are the goals? Use at least one figure.
How does FEM contribute to the project
(Step 2) Katia and Bas will use your proposals to formulate N projects
(Step 3) You form groups of 2-3 students and choose a project
(Step 4) Intermediate report + presentation (April 1 in class)
(Step 5) Final report + presentation (Reading Period)

15. ES 128 Project
The project contributes 25% of the grade, distributed as follows:
10 % April 1, in class. Intermediate presentation (10 minutes) + report.
15%: Reading period Final 15 minute project presentation. Final project report is due

16. Some previous project titles
Diffusion and pattern formation in biology
Analysis of a goat pen gate
Blast loading on sandwich beam structure
Wind turbine blade
Analysis of human femur
Rejection seats
Gas gun

17. Governed by differential equations
Engineering Design
Physical Problem
Question regarding the problem
...how large are the deformations?
...how much is the heat transfer?
Mathematical model
Governed by differential equations
Assumptions regarding
Geometry
Kinematics
Material law
Loading
Boundary conditions
Etc.

18. Engineering Design
The mathematical model is often too complicated to solve by hand. We therefore solve it using a numerical technique - the finite element method.
Physical Problem
Mathematical model
Governed by differential equations
Numerical model
e.g., finite element model

19. Engineering Design Physical Problem Mathematical Model Numerical model
Change physical problem
Mathematical Model
Improve mathematical model
Numerical model
Does answer
make sense?
No!
Refine analysis
Design improvements
Structural optimization
YES!

20. Finite element method Preprocessing Analysis Postprocessing Step 1

21. Preprocessing
The problem domain is subdivided into finite elements

22. Analysis
Step 1: Element formulation - development of equations for the elements
Step 2: Assembly – from equations of a single elements to equations of the entire system
Step 3: Solution of the equations
A x= b
Element
Node

23. Postprocessing
Determination of quantities of interest (such us stress and strain and their visualization)

24. Comments
The numerical solution is only as accurate as the mathematical model
For a well-posed mathematical problem the numerical technique should always, for a reasonable discretization, give a reasonable solution which must converge to the accurate solution as the discretization is refined.

25. We’ll start from…..Trusses

26. Bridge
How does the bridge deform under theses applied forces? P1 P2